Question: $ F = \left[\begin{array}{r}-2 \\ -2 \\ -1\end{array}\right]$ $ E = \left[\begin{array}{r}3 \\ 4 \\ 3\end{array}\right]$ Is $ F- E$ defined?
In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ F$ is of dimension $( m \times  n)$ and $ E$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ F$ ) must equal $ p$ (number of rows in $ E$ ) and 2. $ n$ (number of columns in $ F$ ) must equal $ q$ (number of columns in $ E$ Do $ F$ and $ E$ have the same number of rows? Yes Yes No Yes Do $ F$ and $ E$ have the same number of columns? Yes Yes No Yes Since $ F$ has the same dimensions $(3\times1)$ as $ E$ $(3\times1)$, $ F- E$ is defined.